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Viscous synergic behaviour andsolvent–solvent interactions occurringin liquid mixtures of aqueous alkanolswith some alkanoic acidsMahendra Nath Roy a , Gargi Ghosh a & Lovely Sarkar aa Department of Chemistry , North Bengal University , Darjeeling734013, West Bengal, IndiaPublished online: 29 Oct 2010.

To cite this article: Mahendra Nath Roy , Gargi Ghosh & Lovely Sarkar (2010) Viscous synergicbehaviour and solvent–solvent interactions occurring in liquid mixtures of aqueous alkanols withsome alkanoic acids, Physics and Chemistry of Liquids: An International Journal, 48:5, 564-579, DOI:10.1080/00319100903161507

To link to this article: http://dx.doi.org/10.1080/00319100903161507

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Physics and Chemistry of LiquidsVol. 48, No. 5, October 2010, 564–579

Viscous synergic behaviour and solvent–solvent interactions

occurring in liquid mixtures of aqueous alkanols with

some alkanoic acids

Mahendra Nath Roy*, Gargi Ghosh and Lovely Sarkar

Department of Chemistry, North Bengal University, Darjeeling 734013,West Bengal, India

(Received 10 June 2009; final version received 5 July 2009)

The densities and viscosities of six ternary mixtures of the water, mono-alkanols; 1-propanol, 2-propanol and monoalkanoic acids; formic acid,acetic acid and propionic acid are determined over the entire rangeof composition at 298.15, 308.15 and 318.15K. From the experimentalobservations, the viscous synergy and synergy interaction index are derivedfrom the equations developed by Kalentunc-Gencer, Peleg and Howell,respectively. The speeds of the sound of these ternary mixtures have beenmeasured over the whole composition range at the same temperatures,and also the excess molar volumes, the isentropic compressibilitiesand excess isentropic compressibilities have been evaluated from theexperimental data.

Keywords: synergy; water–monoalkanol–acid system; density; viscosity;ultrasonic speed

1. Introduction

Water is the most widely used solvent in the chemical and pharmaceutical industry,since it is the most physiological and best tolerated excipient. However, in somecases water cannot be used as a solvent because the active substance or solute isinsoluble or slightly soluble in water. For this and other reasons, solvents possessingthe common characteristics of being soluble or mixable in water, may be used; asa result, such solvents can be used for the preparation of binary and tertiarymixtures, etc., with different purposes such as increasing water solubility, ormodifying the viscosity or absorption of the dissolved substances [1]. For example,alcohol and acid solutions are widely used with water in pharmaceutical industryas solvents for their hydrophilic (polar) and protic nature. The increasing useof monoalkanols and their aqueous mixtures in many industrial processes suchas pharmaceutical and cosmetics has greatly stimulated the need for extensiveinformation on their properties. Rheology, the branch of science studies the materialdeformation and flow, is increasingly applied to analyse the viscous behaviour ofmany pharmaceutical products [2–6]. In addition, the rheological and molecularbehaviours of a formulation can influence aspects such as patient acceptability,

*Corresponding author. Email: mahendraroy2002@yahoo.co.in

ISSN 0031–9104 print/ISSN 1029–0451 online

� 2010 Taylor & Francis

DOI: 10.1080/00319100903161507

http://www.informaworld.com

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since it has been well demonstrated that both viscosity and density influence theabsorption rate of such products in the body [7,8].

The present study investigates and quantifies the viscous synergy in the ternarymixtures of water, alcohols and acids. The sets of ternary mixtures are formedfrom water (A) and propanol (B) taken in combination with acids (C); formic acid(set I-a), acetic acid (set I-b), propanoic acid (set I-c) and again from water (A)and isopropanol (B) taken in combination with the same acids (C), i.e. formic acid(set II-a), acetic acid (set II-b), propanoic acid (set II-c), respectively. Water (A),monoalkanols (B) and acids (C) have proton donor and proton acceptor groupsleading to self-association in pure state and mutual association in combined statethrough the significant degree of H-bonding [9,10].

2. Experimental

2.1. Sources and purity of samples

All the chemicals used were from Merck (India). Formic acid was treated with boricanhydride to obtain 98% pure acid. Acetic acid was purified by adding some aceticanhydride to react with the water present and then heating for 1 h to just below theboiling point in presence of 2 g of CrO3, whereas propionic acid was dried byfractional distillation. The source and purification of pure alcohols, 1-propanol and2- propanol, have been described earlier [11,12]. Triply distilled water was used forthe experiments. The purity of the chemicals was ascertained by GLC and also bycomparing the experimental values of densities and viscosities with those reported inthe literature [13–24] as listed in Table 1.

2.2. Method

Densities were measured with an Ostwald–Sprengel-type pycnometer havinga bulb volume of about 25 cm3 and an internal diameter of the capillary of about0.1 cm. The pycnometer was calibrated at 298.15K with doubly distilled water.The pycnometer with experimental liquid was equilibrated in a glass-walledthermostated water bath maintained at �0.01K of the desired temperature. Thepycnometer was then removed from the thermostat, properly dried and weighedin an electronic balance with a precision of �0.01mg. Adequate precautions weretaken to avoid evaporation losses during the time of measurements. An average oftriplicate measurement was taken into account. The uncertainty of density valuesis �3� 10�4 g cm�3. The details of the methods and measurement techniques havebeen described earlier [25].

Solvent viscosities were measured by means of a suspended Ubbelohde-typeviscometer, calibrated at 298.15K with doubly distilled water and purified methanolusing density and viscosity values from the literature [26–28]. A thoroughly cleanedand perfectly dried viscometer filled with experimental liquid was placed vertically inthe glass-walled thermostat maintained to �0.01K. After the attainment of thermalequilibrium, efflux times of flow were recorded with a stopwatch correct to �0.1 s.At least three repetitions of each data reproducible to �0.1 s were taken to averagethe flow times. The uncertainty of viscosity values is �0.003 mPa s. The details of themethods and measurement techniques have been described elsewhere [29,30].

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Ultrasonic speeds of sound were determined by multifrequency ultrasonic

interferometer (Mittal Enterprise, New Delhi) working at 1MHz, calibrated with

water, methanol and benzene at 298.15K. The precision of ultrasonic speed

measurements was �0.2m s�1. The temperature stability was maintained within

�0.01K by circulating thermostated water around the cell with a circulating pump.

The details of the methods and techniques have been described earlier [31].

3. Results and discussion

3.1. Viscous synergy

The measurements yielded the viscosity values, �exp, for the different mixtures at

different concentrations (w/w), listed in Table 2 along with the viscosity values, �calc,in the absence of interactions. The method most widely used to analyse the antagonic

and synergic behaviour of various solvent mixtures is that developed by Roy and

Hazra [32] allowing for the quantification of the synergic and antagonic interactions

taking place in mixtures involving variable proportions of the constituent

components. Viscous synergy is the term applied to the interaction between the

components of a system which causes the total viscosity to be greater than the sum of

the viscosities of each component in the system. In contraposition to viscous

synergism, viscous antagonism is defined as the interaction between the components

of a system causing the net viscosity to be less than the sum of the viscosities of each

component in the system. If the total viscosity of the system is equal to the sum of the

Table 1. Comparison of physical properties at different temperatures of the pure solventswith literature data.

�� 10�3 (kgm�3) �� 102 (mPa s) u (m s�1)

Solvent T (K) Exp. Lit. Exp. Lit. Exp. Lit.

Water 298.15 0.9971 0.9971 [13] 0.894 0.8903 [13] 1497.0 1497.4 [41]308.15 0.9941 0.9940 [13] 0.723 0.7190 [13] – –318.15 0.9903 0.9902 [13] 0.599 0.5972 [13] – –

1-Propanol 298.15 0.7996 0.7995 [14,15] 1.940 1.9324 [14,15] 1207.2 1207.2 [42]308.15 0.7916 0.7916 [14,15] 1.560 1.5600 [14,15] – –318.15 0.7832 0.7846 [16] 1.178 1.1500 [16] – –

2-Propanol 298.15 0.7825 0.7808 [17] 2.031 2.0890 [17] 1138.9 1138.9 [43]308.15 0.7723 0.7723 [17] 1.564 1.5640 [17] – –318.15 0.7636 0.7633 [17] 1.190 1.1920 [17] – –

Formic acid 298.15 1.2114 1.2114 [18] 1.470 1.5100 [19] 1097.0 –308.15 1.1997 1.2012 [19] 1.225 1.2500 [19] – –318.15 1.1883 – 1.175 – – –

Acetic acid 298.15 1.0439 1.0438 [21] 1.070 1.0600 [19] 1132.0 –308.15 1.0328 1.0325 [19] 0.978 – – –318.15 1.0218 – 0.859 – – –

Propionic acid 298.15 0.9888 0.9880 [21] 1.013 1.0300 [19] 1172.0 –308.15 0.9770 0.9776 [22] 0.914 0.8900 [19] – –318.15 0.9669 – 0.658 – – –

566 M.N. Roy et al.

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viscosities of each component, the system is said to lack interaction [33]. The

viscosity in the absence of interaction, �calc, is defined by the ‘simple mixing rule’

�calc ¼X3

i¼1

xi�i, ð1Þ

where xi is the mole fraction and �i is the viscosity, measured experimentally, of the

i-th component. Viscous synergy exists when, �exp4�calc. The procedure is valid for

Newtonian fluids, since in non-Newtonian systems shear rate must be taken into

account and consequently, other synergy indices have been defined [34]. The values

in Table 2 show that �exp4�calc for all the systems, indicating viscous synergy; the

values in Table 2 are graphically represented in Figure 1, where the viscosity is seen

to increase non-linearly for all the mixtures, reaching maximum values (saturation

point) and thereafter to decrease.The explanation of this type of behaviour is based on the known phenomenon of

solvation, as a consequence of the hydrogen bonds formed between the molecules of

the components of the mixture – producing an increase in the size of the resulting

molecular package, which logically implies a rise in viscosity [35]. After reaching the

maximum viscosity, the subsequent addition of more water induces a decrease in

mixture viscosity, as the latter tends to approach the viscosity of water.Such characteristics in the viscosity versus composition curve is a manifestation

of specific interaction [36] between the unlike molecules, predominated by hydrogen

bonding interaction. Maximum viscosity is found in the mixtures when the mole

fractions are in the following ratios:

ðset I-a,II-aÞwater ðAÞþpropanol ðBÞ=isopropanol ðBÞþ formic acid ðCÞ¼ 1:1:35:1:76

ðset I-b,II-bÞwater ðAÞþpropanol ðBÞ=isopropanol ðBÞþacetic acid ðCÞ¼ 1:1:35:1:35

ðset I-c,II-cÞwater ðAÞþpropanol ðBÞ=isopropanol ðBÞþpropionic acid ðCÞ¼ 1:1:35:1:09:

It can be concluded that the affinity of monoalkanoic acid molecules towards

monoalkanols in the presence of water is enhanced by the following order:

Aþ BþHCOOH4Aþ Bþ CH3COOH4Aþ Bþ CH3CH2COOH:

The monoalkanols with hydroxyl group positioned at the second carbon atom

accept more acid and water than those with the terminal hydroxyl group. Similar

results were also reported earlier by Herraez and Belda [17].

3.2. Synergy interaction index

The corresponding viscosity increment given by D�¼ �exp� �calc and the synergy

interaction indices, IS, introduced by Howell [34] is calculated by the following

equation:

IS ¼ ð�exp � �calcÞ=�calc ¼ D�=�calc: ð2Þ

The values recorded in Tables 2 and 3 allow us to plot the graphical

representations shown in Figures 2–5. Figures 2 and 4 show the variations of

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Table 2. Comparison of experimental and calculated viscosities (�) for the indicated water(A)-soluble mixtures of monoalkanols (B) and acids (C) as a function of mass % of water at298.15, 308.15 and 318.15K.

298.15K 308.15K 318.15K

Mass % ofH2O

�exp� 102

(mPas)�calc� 102

(mPas)�exp� 102

(mPas)�calc� 102

(mPas)�exp� 102

(mPas)�calc� 102

(mPas)

HCOOHþ 1-PrOH (w/w¼ 1 : 1)0 1.795 1.617 1.508 1.370 1.270 1.16410 1.845 1.441 1.540 1.213 1.295 1.02720 1.736 1.313 1.443 1.098 1.213 0.92730 1.570 1.217 1.292 1.012 1.082 0.85140 1.407 1.141 1.152 0.944 0.963 0.79250 1.272 1.079 1.042 0.889 0.867 0.74460 1.165 1.029 0.951 0.844 0.792 0.70570 1.072 0.987 0.871 0.806 0.719 0.67280 1.005 0.951 0.813 0.774 0.671 0.64490 0.947 0.920 0.767 0.747 0.634 0.620100 0.894 0.894 0.723 0.723 0.599 0.599

HCOOHþ 2-PrOH (w/w¼ 1 : 1)0 1.888 1.656 1.546 1.372 1.328 1.18210 1.927 1.471 1.575 1.214 1.342 1.04020 1.847 1.336 1.509 1.099 1.276 0.93730 1.699 1.234 1.381 1.013 1.164 0.85940 1.545 1.154 1.254 0.944 1.048 0.79850 1.374 1.090 1.110 0.889 0.933 0.74960 1.227 1.037 0.987 0.844 0.823 0.70870 1.117 0.992 0.899 0.806 0.749 0.67480 1.031 0.954 0.829 0.774 0.688 0.64590 0.962 0.922 0.769 0.747 0.639 0.620100 0.894 0.894 0.723 0.723 0.599 0.599

CH3COOHþ 1-PrOH (w/w¼ 1 : 1)0 1.755 1.655 1.333 1.269 1.049 1.00410 1.765 1.449 1.352 1.121 1.072 0.89520 1.644 1.309 1.273 1.020 1.021 0.82030 1.453 1.207 1.130 0.947 0.910 0.76640 1.297 1.130 1.016 0.892 0.826 0.72550 1.175 1.069 0.924 0.849 0.750 0.69260 1.088 1.021 0.856 0.814 0.699 0.66670 1.013 0.980 0.806 0.785 0.661 0.64580 0.960 0.947 0.768 0.761 0.633 0.62790 0.922 0.918 0.743 0.740 0.614 0.612100 0.894 0.894 0.723 0.723 0.599 0.599

CH3COOHþ 2-PrOH (w/w¼ 1 : 1)0 1.835 1.700 1.358 1.271 1.087 1.02410 1.846 1.482 1.382 1.123 1.109 0.90920 1.709 1.334 1.299 1.022 1.054 0.83130 1.510 1.226 1.160 0.949 0.942 0.77440 1.346 1.144 1.042 0.893 0.848 0.73150 1.218 1.080 0.949 0.849 0.773 0.69760 1.116 1.028 0.876 0.814 0.718 0.67070 1.038 0.986 0.818 0.785 0.673 0.647

(continued )

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Table 2. Continued.

298.15K 308.15K 318.15K

Mass % ofH2O

�exp� 102

(mPas)�calc� 102

(mPas)�exp� 102

(mPas)�calc� 102

(mPas)�exp� 102

(mPas)�calc� 102

(mPas)

80 0.978 0.950 0.777 0.761 0.640 0.62990 0.932 0.920 0.746 0.740 0.617 0.613100 0.894 0.894 0.723 0.723 0.599 0.599

CH3CH2COOHþ 1-PrOH (w/w¼ 1 : 1)0 1.712 1.691 1.327 1.320 0.933 0.93010 1.616 1.460 1.262 1.146 0.913 0.83420 1.476 1.309 1.160 1.034 0.863 0.77130 1.308 1.203 1.032 0.954 0.783 0.72740 1.182 1.125 0.934 0.895 0.722 0.69550 1.092 1.064 0.866 0.850 0.679 0.66960 1.031 1.016 0.822 0.814 0.654 0.65070 0.983 0.977 0.789 0.785 0.636 0.63380 0.948 0.944 0.763 0.761 0.622 0.62090 0.918 0.917 0.741 0.740 0.609 0.609100 0.894 0.894 0.723 0.723 0.599 0.599

CH3CH2COOHþ 2-PrOH (w/w¼ 1 : 1)0 1.810 1.742 1.361 1.322 0.977 0.95210 1.714 1.495 1.309 1.148 0.949 0.83420 1.570 1.335 1.212 1.035 0.902 0.77130 1.378 1.223 1.070 0.955 0.812 0.72740 1.228 1.139 0.960 0.896 0.741 0.69550 1.127 1.075 0.884 0.851 0.692 0.66960 1.050 1.024 0.831 0.814 0.660 0.65070 0.994 0.982 0.793 0.785 0.639 0.63380 0.953 0.948 0.765 0.761 0.624 0.62090 0.921 0.919 0.742 0.740 0.610 0.609100 0.894 0.894 0.723 0.723 0.599 0.599

0.85

1.05

1.25

1.45

1.65

1.85

0 20 40 60 80 100

Mass % of H2O

h (m

Pa

s)

Figure 1. Experimental and calculated viscosity (�) of: (s), water (A)þ propanol (B)þformic acid (C); (m), water (A)þ 2-propanol (B)þ formic acid (C); (�), water (A)þ propanol(B)þ acetic acid (C); (^), water (A)þ 2-propanol (B)þ acetic acid (C); (�), water(A)þ propanol (B)þ propionic acid (C); (.), water (A)þ 2-propanol (B)þ propionic acid(C) mixtures with mass % of water (A) at 298.15K, exp (—), calc (- - -).

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D� and IS with increasing mass % of water. These graphs also show the same trend asshown by the viscosity curves.

Figure 3 represents the viscosities �max, as a function of the number of carbonatoms for the alkanoic acids and shows that the values of �max decrease almostlinearly with the number of carbon atoms. For the monoalkanol with the hydroxylgroup at the second carbon atom, expected to be greater than primary monoalkanol,also decreases in the same way. Similar results were reported in an earlier paper [35].

Figures 4 and 5 show the viscous synergy interaction index, IS, as a function ofmass % of H2O and the number of carbon atoms corresponding to themonoalkanols with the hydroxyl group at the end of the molecular chain and thesecond carbon atom, respectively. These figures show that the synergic indices of themonoalkanoic acids in aqueous monoalkanols follow the order:

Aþ BþHCOOH4Aþ Bþ CH3COOH4Aþ Bþ CH3CH2COOH

showing the same trend as D� values and monoalkanols with the hydroxyl groupat the second carbon atom of the molecular chain due to more symmetric nature aregreater than those of the monoalkanols with terminal hydroxyl group. Similar resultsreported earlier [17,35] are in excellent agreement with the results obtained from theviscosity values recorded in this article.

The gradual decrement of synergy interaction values from HCOOH toCH3CH2COOH can be explained in view of þI-effect. –C2H5 has more þI-effectthan –CH3 which has in turn than –H. This facilitates more interactions of HCOOHwith unlike molecules than CH3COOH and CH3CH2COOH rendering to highervalues of synergy interaction parameters.

3.3. Excess molar volume

The experimentally determined density values along with the derived parameter, VE,the excess molar volume, are listed in Table 4.

The excess molar volumes, VE, are calculated from density data according to thefollowing equation [37]:

VE ¼X3

i¼1

xiMið1=�� 1=�iÞ, ð3Þ

where Mi, �i and � are the molar mass, density of the i-th component and density ofthe mixture, respectively.

Figure 6 represents the VE values for the six ternary mixtures under experiment.In general, VE is found to be negative throughout all the temperatures for all theternary mixtures. However, the value at first decreases to a minima and then it

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Table 3. Deviation in viscosity (D�) and viscous synergy interaction index (IS) values for theternary liquid mixtures of water (A)þmonoalkanols (B)þ acids (C) at 298.15, 308.15 and318.15K.

298.15K 308.15K 318.15K

Mass % ofH2O

D�� 102

(mPas)IS D�� 102

(mPas)IS D�� 102

(mPas)IS

HCOOHþ 1-PrOH (w/w¼ 1 : 1)0 0.178 0.110 0.138 0.101 0.106 0.09110 0.404 0.280 0.327 0.270 0.268 0.26120 0.422 0.322 0.345 0.314 0.286 0.30930 0.354 0.291 0.280 0.277 0.231 0.27140 0.267 0.234 0.208 0.220 0.171 0.21650 0.192 0.178 0.153 0.172 0.123 0.16660 0.136 0.132 0.107 0.127 0.087 0.12470 0.085 0.086 0.065 0.081 0.047 0.07080 0.054 0.056 0.039 0.050 0.028 0.04390 0.027 0.029 0.020 0.027 0.014 0.023

100 0.000 0.000 0.000 0.000 0.000 0.000

HCOOHþ 2-PrOH (w/w¼ 1 : 1)0 0.232 0.140 0.174 0.127 0.146 0.12410 0.456 0.310 0.361 0.297 0.302 0.29120 0.510 0.382 0.409 0.372 0.339 0.36230 0.465 0.377 0.368 0.364 0.305 0.35540 0.391 0.338 0.309 0.328 0.250 0.31350 0.284 0.261 0.221 0.249 0.185 0.24760 0.190 0.183 0.143 0.170 0.116 0.16370 0.125 0.126 0.093 0.115 0.075 0.11180 0.077 0.081 0.055 0.071 0.043 0.06690 0.040 0.043 0.023 0.031 0.019 0.030

100 0.000 0.000 0.000 0.000 0.000 0.000

CH3COOHþ 1-PrOH (w/w¼ 1 : 1)0 0.100 0.060 0.064 0.050 0.045 0.04410 0.316 0.218 0.231 0.206 0.177 0.19820 0.335 0.256 0.252 0.247 0.201 0.24530 0.246 0.204 0.183 0.193 0.144 0.18840 0.167 0.148 0.124 0.139 0.101 0.13950 0.106 0.099 0.075 0.089 0.058 0.08360 0.067 0.066 0.043 0.053 0.033 0.04970 0.032 0.033 0.022 0.028 0.016 0.02580 0.013 0.014 0.008 0.010 0.006 0.01090 0.004 0.004 0.003 0.004 0.003 0.004

100 0.000 0.000 0.000 0.000 0.000 0.000

CH3COOHþ 2-PrOH (w/w¼ 1 : 1)0 0.135 0.079 0.087 0.068 0.063 0.06110 0.364 0.245 0.259 0.231 0.199 0.21920 0.375 0.281 0.277 0.271 0.224 0.26930 0.284 0.232 0.211 0.223 0.168 0.21740 0.202 0.176 0.150 0.168 0.117 0.16050 0.138 0.128 0.100 0.117 0.076 0.10960 0.088 0.086 0.062 0.076 0.048 0.072

(continued )

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Table 3. Continued.

298.15K 308.15K 318.15K

Mass % ofH2O

D�� 102

(mPas)IS D�� 102

(mPas)IS D�� 102

(mPas)IS

70 0.053 0.053 0.033 0.043 0.026 0.04080 0.028 0.029 0.016 0.021 0.012 0.01990 0.012 0.013 0.006 0.008 0.005 0.007

100 0.000 0.000 0.000 0.000 0.000 0.000

CH3CH2COOHþ 1-PrOH (w/w¼ 1 : 1)0 0.021 0.012 0.007 0.005 0.004 0.00410 0.156 0.107 0.116 0.101 0.079 0.09520 0.167 0.127 0.126 0.122 0.092 0.11930 0.105 0.087 0.078 0.082 0.056 0.07740 0.057 0.051 0.039 0.043 0.028 0.04050 0.028 0.026 0.016 0.019 0.010 0.01560 0.015 0.015 0.008 0.010 0.005 0.00770 0.007 0.007 0.004 0.005 0.002 0.00480 0.004 0.004 0.003 0.004 0.002 0.00390 0.001 0.001 0.001 0.001 0.001 0.001

100 0.000 0.000 0.000 0.000 0.000 0.000

CH3CH2COOHþ 2-PrOH (w/w¼ 1 : 1)0 0.069 0.039 0.039 0.030 0.025 0.02610 0.219 0.146 0.161 0.140 0.116 0.13920 0.235 0.176 0.178 0.172 0.131 0.17030 0.155 0.127 0.114 0.120 0.085 0.11640 0.089 0.078 0.064 0.071 0.046 0.06750 0.052 0.048 0.033 0.039 0.023 0.03460 0.026 0.025 0.017 0.021 0.011 0.01670 0.012 0.012 0.008 0.010 0.006 0.00980 0.005 0.005 0.004 0.006 0.004 0.00690 0.002 0.002 0.002 0.002 0.001 0.002

100 0.000 0.000 0.000 0.000 0.000 0.000

–0.05

0.05

0.15

0.25

0.35

0.45

0.55

0 20 40 60 80 100

Mass % of H2O

Δh (

mP

a s)

Figure 2. Viscosity deviation (D�) of: (s), water (A)þ propanol (B)þ formic acid (C); (^),water (A)þ 2-propanol (B)þ formic acid (C); (D), water (A)þ propanol (B)þ acetic acid (C);(m), water (A)þ 2-propanol (B)þ acetic acid (C); (�), water (A)þ propanol (B)þ propionicacid (C); (.), water (A)þ 2-propanol (B)þ propionic acid (C) mixtures with mass% of water(A) at 298.15K.

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0.00 20 40 60 80 100

0.10.10.20.20.30.30.40.40.5

Mass % of H2O

I s

Figure 4. Viscous synergy interaction index (IS) values of: (s), water (A)þ propanol(B)þ formic acid (C); (^), water (A)þ 2-propanol (B)þ formic acid (C); (D), water(A)þ propanol (B)þ acetic acid (C); (m), water (A)þ 2-propanol (B)þ acetic acid (C);(�), water (A)þ propanol (B)þ propionic acid (C); (.), water (A)þ 2-propanol (B)þpropionic acid (C) mixtures with mass% of water (A) at 298.15K.

032 2.51.51

0.050.1

0.150.2

0.250.3

0.350.4

NC

I S

Figure 5. Viscous synergy interaction index (IS) of the monoalkanoic acids as a function of thenumber of carbon atoms, NC, for water (A)þ propanol (B), (––^––); water (A)þ 2-propanol(B), (- - -g- - -) systems.

1.61 2 32.51.5

1.651.7

1.751.8

1.851.9

1.95

NC

h max

(mP

a s)

Figure 3. �max of the monoalkanoic acids as a function of the number of carbon atoms,NC, for water (A)þ propanol (B), (––^––); water (A)þ 2-propanol (B), (- - -g- - -) systems at298.15K.

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Table 4. Comparison of experimental densities (�) and excess molar volumes (VE) for theindicated water (A)-soluble mixtures of monoalkanols (B) and acids(C) as a function ofmass% at 298.15, 308.15 and 318.15K.

298.15K 308.15K 318.15K

Mass % ofH2O

�exp� 10�3

(kgm�3)VE� 103

(m3mol�1)�exp� 10�3

(kg m�3)VE� 103

(m3mol�1)�exp� 10�3

(kg m�3)VE� 103

(m3mol�1)

HCOOHþ 1-PrOH (w/w¼ 1 : 1)0 0.9770 �0.7570 0.9668 �0.7330 0.9565 �0.714010 0.9936 �1.2320 0.9833 �1.1910 0.9733 �1.175020 1.0034 �1.3010 0.9938 �1.2730 0.9842 �1.257030 1.0075 �1.1620 0.9982 �1.1260 0.9873 �1.047040 1.0085 �0.9620 0.9994 �0.9140 0.9875 �0.794050 1.0059 �0.7060 0.9986 �0.6900 0.9878 �0.593060 1.0036 �0.5020 0.9966 �0.4760 0.9881 �0.427070 1.0014 �0.3330 0.9960 �0.3290 0.9883 �0.286080 0.9996 �0.1980 0.9940 �0.1740 0.9885 �0.167090 0.9981 �0.0870 0.9934 �0.0680 0.9888 �0.0660100 0.9971 0.0000 0.9941 0.0000 0.9903 0.0000

HCOOHþ 2-PrOH (w/w¼ 1 : 1)0 0.9656 �0.8390 0.9540 �0.8330 0.9437 �0.829010 0.9832 �1.3040 0.9714 �1.2680 0.9610 �1.245020 0.9946 �1.3810 0.9833 �1.3440 0.9734 �1.327030 1.0012 �1.2730 0.9903 �1.2270 0.9807 �1.202040 1.0034 �1.0560 0.9925 �0.9890 0.9841 �0.982050 1.0029 �0.8090 0.9927 �0.7420 0.9851 �0.738060 1.0012 �0.5770 0.9928 �0.5370 0.9860 �0.535070 0.9998 �0.3890 0.9930 �0.3670 0.9869 �0.364080 0.9986 �0.2340 0.9931 �0.2210 0.9878 �0.220090 0.9976 �0.1040 0.9932 �0.0950 0.9886 �0.0930100 0.9971 0.0000 0.9941 0.0000 0.9903 0.0000

CH3COOHþ 1-PrOH (w/w¼ 1 : 1)0 0.9120 �0.4700 0.9023 �0.4510 0.8920 �0.400010 0.9316 �1.0100 0.9219 �0.9780 0.9120 �0.948020 0.9454 �1.0760 0.9360 �1.0410 0.9268 �1.031030 0.9547 �0.9340 0.9456 �0.8930 0.9370 �0.888040 0.9613 �0.7300 0.9526 �0.6860 0.9446 �0.681050 0.9665 �0.5250 0.9595 �0.5170 0.9518 �0.503060 0.9725 �0.3800 0.9665 �0.3800 0.9598 �0.378070 0.9780 �0.2470 0.9720 �0.2300 0.9660 �0.228080 0.9830 �0.1230 0.9777 �0.1070 0.9724 �0.105090 0.9896 �0.0490 0.9847 �0.0270 0.9801 �0.0250100 0.9971 0.0000 0.9941 0.0000 0.9903 0.0000

CH3COOHþ 2-PrOH (w/w¼ 1 : 1)0 0.9020 �0.5590 0.8908 �0.5380 0.8800 �0.466010 0.9230 �1.1210 0.9120 �1.0950 0.9020 �1.074020 0.9380 �1.1810 0.9272 �1.1430 0.9175 �1.120030 0.9480 �1.0100 0.9379 �0.9770 0.9288 �0.960040 0.9560 �0.8050 0.9462 �0.7590 0.9375 �0.737050 0.9620 �0.5800 0.9537 �0.5600 0.9456 �0.539060 0.9690 �0.4240 0.9619 �0.4150 0.9538 �0.3780

(continued )

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Table 4. Continued.

298.15K 308.15K 318.15K

Mass % ofH2O

�exp� 10�3

(kgm�3)VE� 103

(m3mol�1)�exp� 10�3

(kg m�3)VE� 103

(m3mol�1)�exp� 10�3

(kg m�3)VE� 103

(m3mol�1)

70 0.9750 �0.2690 0.9686 �0.2550 0.9609 �0.214080 0.9810 �0.1370 0.9760 �0.1350 0.9694 �0.107090 0.9880 �0.0440 0.9840 �0.0430 0.9787 �0.0280100 0.9971 0.0000 0.9941 0.0000 0.9903 0.0000

CH3CH2COOHþ 1-PrOH (w/w¼ 1 : 1)0 0.8838 0.0160 0.8742 0.0330 0.8649 0.045010 0.9040 �0.6390 0.8943 �0.6000 0.8850 �0.576020 0.9195 �0.7780 0.9100 �0.7350 0.9011 �0.718030 0.9313 �0.6970 0.9224 �0.6630 0.9140 �0.651040 0.9413 �0.5620 0.9329 �0.5280 0.9251 �0.521050 0.9500 �0.4090 0.9421 �0.3740 0.9344 �0.353060 0.9590 �0.2920 0.9513 �0.2470 0.9441 �0.226070 0.9670 �0.1680 0.9605 �0.1400 0.9542 �0.127080 0.9760 �0.0840 0.9706 �0.0660 0.9653 �0.063090 0.9860 �0.0300 0.9815 �0.0160 0.9769 �0.0140100 0.9971 0.0000 0.9941 0.0000 0.9903 0.0000

CH3CH2COOHþ 2-PrOH (w/w¼ 1 : 1)0 0.8742 �0.0660 0.8629 �0.0200 0.8535 �0.017010 0.8960 �0.7650 0.8848 �0.7150 0.8755 �0.706020 0.9127 �0.9000 0.9019 �0.8540 0.8929 �0.844030 0.9256 �0.8060 0.9152 �0.7560 0.9064 �0.736040 0.9360 �0.6310 0.9267 �0.6010 0.9185 �0.587050 0.9455 �0.4610 0.9371 �0.4380 0.9291 �0.412060 0.9554 �0.3310 0.9480 �0.3150 0.9412 �0.309070 0.9642 �0.1930 0.9581 �0.1890 0.9519 �0.182080 0.9743 �0.1040 0.9686 �0.0880 0.9631 �0.082090 0.9843 �0.0220 0.9799 �0.0150 0.9753 �0.0130100 0.9971 0.0000 0.9941 0.0000 0.9903 0.0000

–1.6

–1.4

–1.2

–1.0

–0.8

–0.6

–0.4

–0.2

0.00 20 40 60 80 100

Mass % of H2O

VEx

103

(m3

mol

–1)

Figure 6. Excess molar volumes (VE) of: (s), water (A)þ propanol (B)þ formic acid (C);(^), water (A)þ 2-propanol (B)þ formic acid (C); (D), water (A)þ propanol (B)þ aceticacid (C); (m), water(A)þ 2-propanol (B)þ acetic acid (C); (�), water (A)þ propanol(B)þ propionic acid (C); (.), water (A)þ 2-propanol (B)þ propionic acid (C) mixtures withmass% of water (A) at 298.15K.

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increases with increasing mass% of water. VE increases systematically from 298.15 to318.15K over the whole range of compositions. The six ternary mixtures show theminima in the range of xA¼ 0.4� 0.5 with an exception in set (I-c, II-c) which showsminima at xA¼ 0.6. The trend is:

Aþ ðBÞ þ CH3CH2COOH4Aþ ðBÞ þ CH3COOH4Aþ ðBÞ þHCOOH:

The negative VE indicates the presence of strong molecular interaction betweenthe components of the mixture. Several effects contribute to the value of VE, such as[38]: (1) dipolar interaction, (2) interstitial accommodation of one component intothe other and (3) possible hydrogen-bonded interactions between unlike molecules.The actual volume change would, therefore, depend on the relative strength of thesethree effects.

3.4. Deviation in isentropic compressibility

Isentropic compressibility, KS and deviation in isentropic compressibility, K ES were

calculated using the following relations

KS ¼ 1=ðu2�expÞ ð4Þ

K ES ¼ KS �

X3

i¼1

xiKS,i, ð5Þ

where u and KS are the speed of sound, isentropic compressibility of the mixture andKS,i, the isentropic compressibility of the i-th component in the mixture. Theexperimental speed of sound, isentropic compressibility and deviation in isentropiccompressibility are listed in Table 5 and are graphically represented in Figure 7 asa function of mass % of water.

Figure 7 shows that K ES values are negative for all the mixtures under

investigation, and they increase as the length of the molecular chain of themonoalkanoic acid increases. The donor–acceptor interactions between the mixingcomponents play a pivotal role to yield negative K E

S values, which are morenegative for the lower monoalkanoic acids. However, the branched isomers havelower K E

S values than their terminal counter parts, as they can fit well into thestructure of the acids and water. Similar results were reported by some authors[35,39,40] previously.

4. Conclusion

In summary, monoalkanoic acids containing up to three carbon atoms mix withwater and monoalkanol mixture in any proportion, but the synergic interactions tendto decrease with the increase of C atoms in the chain. The monoalkanols with thehydroxyl group positioned at the second carbon atom accept more water and acidsthan those with the terminal hydroxyl group and their IS, values are, therefore,considerably higher.

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Table 5. Speeds of sound (u), isentropic compressibilities (KS) and deviation in isentropiccompressibilities (K E

S ) of ternary mixtures for various compositions of (A)þ (B)þ (C) at298.15K.

Mass % ofH2O

u(m s�1)

KS� 1012

(Pa�1)K E

S � 1012

(Pa�1)u

(m s�1)KS� 1012

(Pa�1)K E

S � 1012

(Pa�1)

HCOOHþ 1-PrOH (w/w¼ 1 : 1) HCOOHþ 2-PrOH (w/w¼ 1 : 1)

0 1141.5 785.5 2.5 1112.0 837.5 2.210 1205.7 692.3 0.8 1179.1 731.6 0.520 1270.5 617.4 �1.2 1247.2 646.4 �1.530 1332.1 559.3 �2.8 1309.6 582.4 �3.040 1384.1 517.6 �3.7 1366.0 534.1 �3.950 1425.5 489.2 �3.9 1410.6 501.1 �4.160 1457.5 469.1 �3.7 1447.0 477.0 �3.970 1475.3 458.8 �3.0 1471.5 461.9 �3.380 1484.5 454.0 �1.9 1485.3 453.9 �2.390 1491.8 450.2 �0.9 1492.8 449.8 �1.1100 1497.0 447.5 0.0 1497.0 447.5 0.0

CH3COOHþ 1-PrOH (w/w¼ 1 : 1) CH3COOHþ 2-PrOH (w/w¼ 1 : 1)

0 1147.4 832.9 3.0 1114.0 893.4 2.710 1221.8 719.1 1.2 1191.1 763.7 1.020 1291.5 634.2 �0.7 1265.6 665.6 �1.030 1356.1 569.6 �2.4 1334.1 592.7 �2.740 1409.1 523.9 �3.4 1390.1 541.3 �3.650 1447.5 493.8 �3.6 1433.0 506.2 �3.860 1472.6 474.2 �3.3 1463.2 482.0 �3.570 1484.2 464.2 �2.4 1478.3 469.3 �2.680 1490.0 458.2 �1.4 1488.0 460.4 �1.690 1493.0 453.3 �0.6 1493.0 454.1 �0.7100 1497.0 447.5 0.0 1497.0 447.5 0.0

CH3CH2COOHþ 1-PrOH (w/w¼ 1 : 1) CH3CH2COOH+2-PrOH (w/w¼ 1 : 1)

0 1162.0 838.0 3.5 1124.0 905.4 3.210 1242.1 717.0 1.7 1208.8 763.8 1.420 1313.3 630.6 �0.2 1284.2 664.4 �0.530 1376.1 567.0 �1.9 1352.4 590.7 �2.240 1427.1 521.7 �2.9 1408.0 538.9 �3.250 1461.0 493.1 �3.0 1446.7 505.3 �3.360 1478.6 476.9 �2.5 1469.0 485.0 �2.870 1487.3 467.5 �1.7 1481.5 472.5 �1.980 1491.0 460.9 �0.9 1486.2 464.7 �1.090 1493.0 455.0 �0.3 1493.2 455.7 �0.4100 1497.0 447.5 0.0 1497.0 447.5 0.0

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Acknowledgements

The authors are grateful to the departmental special assistance scheme under the UniversityGrants Commission, New Delhi (No. F 540/27/DRS/2007, SAP-1) for financial support.L. Sarkar is also grateful to UGC Research Fellowship in Science Ref. UGC letter No. F.4 -1/2006 (X1 plan/BSR) for sanctioning a junior research fellowship and providing financial aid insupport of this research work.

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Pa–1

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Figure 7. Deviation in isentropic compressibility (K ES ) of: (s), water (A)þ propanol

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